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A. Shovels and Swords

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPolycarp plays a well-known computer game (we won't mention its name). In this game, he can craft tools of two types — shovels and swords. To craft a shovel, Polycarp spends two sticks and one diamond; to craft a sword, Polycarp spends two diamonds and one stick.

Each tool can be sold for exactly one emerald. How many emeralds can Polycarp earn, if he has $$$a$$$ sticks and $$$b$$$ diamonds?

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases.

The only line of each test case contains two integers $$$a$$$ and $$$b$$$ ($$$0 \le a, b \le 10^9$$$) — the number of sticks and the number of diamonds, respectively.

Output

For each test case print one integer — the maximum number of emeralds Polycarp can earn.

Example

Input

4 4 4 1000000000 0 7 15 8 7

Output

2 0 7 5

Note

In the first test case Polycarp can earn two emeralds as follows: craft one sword and one shovel.

In the second test case Polycarp does not have any diamonds, so he cannot craft anything.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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